Abstract
Reinforcement learning using verifiable rewards (RLVR) improves LLM reasoning, but the conditions under which it transfers across domains -- and why it does so -- remain under-explored. We study cross-domain transfer in a 7B model whose SFT and RL post-training stages use only constraint-satisfaction puzzles, with no mathematics problems in the post-training data. To analyze how transfer emerges, we introduce a reasoning primitive-level framework that combines a 9-class span classifier with motif extraction, allowing us to segment chain-of-thought traces into primitive motifs and track their evolution across training stages and domains. We find that puzzle SFT induces a reasoning-primitive vocabulary, yielding a pp \texttt{pass@32} gain on OlymMATH-Hard. Vanilla GSPO then composes these primitives into longer compute-verify chains, adding a further pp. However, this RL stage also suppresses exploratory primitives such as \textit{hypothesize} and \textit{backtrack}. To address this, we introduce a novelty bonus that rewards diverse correct rollouts, using perplexity under the reference model as a signal. This restores recovery primitives during RL and adds a further pp \texttt{pass@32} relative to vanilla GSPO. Finally, the end-to-end recipe raises the hard-math capability ceiling from at the OLMo3-7B-Instruct-SFT base to , without adding any mathematics problems during the SFT or RL stages.